ELECTRICITY, MAGNETISM AND ELECTROMAGNETICS: JAMES CLERK MAXWELL: SYMMETRY AND UNIFICATION IN PHYSICS

Michael Bass College of Optics and Photonics University of Central Florida © M. Bass

Electric charges

• Since the Greeks rubbed one thing on another.

– around 700 BC someone was polishing amber with cats fur and noticed that things like straw and feathers were attracted to it.

– the Greek word for amber is electron – hence electric, electricity, electronics, electron … © M. Bass

Was it the amber itself?

• By 1600 Sir William Gilbert showed that this

property of attracting things

when rubbed was not a property of amber but

was universal

.

– Other stuff showed the same effect.

– Gilbert also showed that the earth was a magnet. • The problem was that no one knew

what was being rubbed

. – Was it a fluid, an essence, or particles?

– Was the process of rubbing creating whatever was responsible for the effect or was it moving something around? © M. Bass

Lightning strikes!

• • • • – Benjamin Franklin showed that the same process as involved in rubbing one thing on another gave rise to lightning. He identified

two types of charges

and negative. and called them positive – The only problem was that he got his signs wrong. The charges that move about are negative not positive charges. – Whatever they were,

charges were very small

.

When there were many they could be thought of as resulting in a continuous distribution in or on an object.

Later it was found that

the smallest increment of free charge that we can find in the universe is that on the electron or 1.6 x 10 -19 coulombs.

This is a description of things to come -

considered quantized

early.

charge was

© M. Bass

Quantify and make measurable

• Charles Augustin Coulomb (1736-1806) • The law of force between point charges is an

inverse square law force

. – The electrostatic force had the same functional form as Newton’s law of gravity – Carl Freidrich Gauss would show this is due to the fact that there are 3 dimensions to space.

• • Introduced a proportionality constant to get the units of force to be the same on both sides of his equation. – The famous e 0 .

Maxwell was to show this constant is related to the speed of light.

© M. Bass

• •

Related but not yet recognized

1803 - Thomas Young reported one of the most brilliant and epochal experiments ever. –

The two slit interference experiment gave incontrovertible proof that light is wavelike.

Keep in mind that Newton, the towering figure of science, considered light to be corpuscular. – 97 years later

Max Planck showed that light has a particle like nature.

Confusing isn’t it? – This problem of duality is inherent in modern quantum mechanics as we will discuss later. – For the time being however, light was wavelike and Young had proved it.

–

Maxwell would show that light was electromagnetic waves.

© M. Bass

What if charges moved?

• Clearly charges could move.

• What happened when charges moved?

– They exerted Coulomb’s force when static.

– What would be observed when they moved?

• How did they interact with each other, with other objects and what effects would result?

• To understand this we have to consider magnetism.

© M. Bass

Magnets

• • • • Magnets (lodestones are natural magnets) had been known for centuries. Since about 2000 BC the Chinese used them to make compasses. The word magnet comes from the name of a city in Turkey, Magnesia, where the mineral magnetite is found.

– It was soon clear that

magnets always have both north and south poles

. No mater how small you divided your magnet it always had both a north and a south. – A modern way of saying this is to say that

no monopoles.

we have never found a magnetic monopole, dipoles yes but

© M. Bass

Moving charges affect magnets

• • • – – In 1820 Hans Christian Oersted observed that

currents (moving electric charges) affected magnets

much the same way as other magnets did.

They exerted forces on the magnets.

He offered no explanation and no numerical measurements. – – Also in 1820 Jean Baptiste Biot and Felix Savart, two Frenchmen demonstrated that the magnetic force due to a current was given by an inverse square law. They introduced another constant to get the units right.

The equally famous m 0 /4 p

Maxwell was to show that it too was related to the speed of light.

© M. Bass

• • •

The genius of Faraday

In London (in a lab I visited in 1997)

bookbinder’s assistant Michael Faraday (1791-1867), an unschooled

, experimented with magnets and currents. – – In 1831 he observed that a moving magnet could induce a current in a circuit.

This is the inverse of Oersted’s observation.

Somehow electricity and magnetism were intimately related!!!

This became Faraday’s law of induction and ultimately one of Maxwell’s equations © M. Bass

Other events of 1831

• Faraday also observed that a changing current could, through its magnetic effects, induce a current to flow in another circuit.

• If you spin a magnet inside a circuit it will generate current – the electric generator .

© M. Bass

The real genius of Faraday

• Since he had no mathematical training but thought geometrically, he • invented the concept of fields of force.

– A geometric means of conceiving of what his experiments were showing him.

• This concept, this interpretation of what he saw is what set him apart from his predecessors.

• It enables modern science!!!!

© M. Bass

James Clerk Maxwell

• • • James Clerk Maxwell had the mathematical skills that Faraday lacked and used them to become

the greatest theoretician of the 19th century

. He graduated Edinburgh University at age 15 and became a full professor at Aberdeen University at age 17. In the 40 years (1839-1879) of his life he established the foundations of electricity and magnetism as

electromagnetics, established the kinetic theory of gasses, explained the rings of Saturn and experimented with color vision

. © M. Bass

• • • • • •

Maxwell’s symmetry and unification

Two rules governed electricity and two other rules governed magnetism. Maxwell noticed that in these laws the electric field and the magnetic field appeared nearly symmetrically in the equations. For example, in Faraday’s Law a time varying magnetic field gave rise to an electric field. In Ampere’s law, as Maxwell modified it, a time varying electric field gave rise to a magnetic field. When made symmetric in electric and magnetic fields the set of four equations described them both, they described the subject we now call electromagnetism.

Electricity and magnetism had been unified into electromagnetism!

© M. Bass

It had to be so

• Maxwell’s equations gave rise to a

wave equation

for waves that propagated at the speed of light.

• Young had shown that light was a wave phenomenon.

• Light had to be an

electromagnetic wave

and so: God said  

E

 e

q

0  

B

 

E

  0  

B



t

 

B

 m 0

J

 m 0 e 0 

E



t

and there was light.

• Remarkably, the speed of light was ( e 0 m 0 ) -1/2 did not have to be referenced to anything.

and © M. Bass

• • • •

All sorts of electromagnetic waves

– Not only did Maxwell’s waves

travel at the speed of light

, they were

polarized

light, they

carried energy

just as is as does light and they

diffracted and interfered

as does light. Faraday, by now an old man, had claimed light was a transverse wave. He had been ridiculed for this. Maxwell visited him to explain that he, Faraday, had been right after all. They also

reflected and refracted

. Clearly, Maxwell’s electromagnetic waves were a form of light. – Later it became clear that so were

radio waves, microwaves and many others

.

See the work of Hertz and Marconi for example.

© M. Bass

• • • • • •

Victory

Light was an electromagnetic wave.

– Hertz and Marconi had shown that so were radio waves.

Einstein was to show that Maxwell’s laws were exactly valid in the relativistic case. •

The only pre-Einstein theory that required no relativistic corrections.

After all it is the theory of light.

A stunning set of victories for the theory and for the notions of symmetry and unification.

The first step towards unification of the different forces that governed our universe. – • Today we believe only 4 forces describe everything: Gravity; Electromagnetism; Weak nuclear; Strong nuclear Maxwell’s principles,

symmetry of form and unification

, are still in use today in science and in our culture in general. © M. Bass